Polytope of Type {10,10,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,10,8}*1600c
if this polytope has a name.
Group : SmallGroup(1600,8648)
Rank : 4
Schlafli Type : {10,10,8}
Number of vertices, edges, etc : 10, 50, 40, 8
Order of s0s1s2s3 : 40
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,10,8}*800, {10,10,4}*800c
4-fold quotients : {5,10,4}*400, {10,10,2}*400c
5-fold quotients : {10,2,8}*320
8-fold quotients : {5,10,2}*200
10-fold quotients : {5,2,8}*160, {10,2,4}*160
20-fold quotients : {5,2,4}*80, {10,2,2}*80
25-fold quotients : {2,2,8}*64
40-fold quotients : {5,2,2}*40
50-fold quotients : {2,2,4}*32
100-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 6, 21)( 7, 25)( 8, 24)( 9, 23)( 10, 22)( 11, 16)
( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)( 32, 50)
( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)
( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 61, 66)
( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)( 82,100)
( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)( 90, 92)
(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)(111,116)
(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)(132,150)
(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)(140,142)
(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)(160,172)(161,166)
(162,170)(163,169)(164,168)(165,167)(177,180)(178,179)(181,196)(182,200)
(183,199)(184,198)(185,197)(186,191)(187,195)(188,194)(189,193)(190,192)
(202,205)(203,204)(206,221)(207,225)(208,224)(209,223)(210,222)(211,216)
(212,220)(213,219)(214,218)(215,217)(227,230)(228,229)(231,246)(232,250)
(233,249)(234,248)(235,247)(236,241)(237,245)(238,244)(239,243)(240,242)
(252,255)(253,254)(256,271)(257,275)(258,274)(259,273)(260,272)(261,266)
(262,270)(263,269)(264,268)(265,267)(277,280)(278,279)(281,296)(282,300)
(283,299)(284,298)(285,297)(286,291)(287,295)(288,294)(289,293)(290,292)
(302,305)(303,304)(306,321)(307,325)(308,324)(309,323)(310,322)(311,316)
(312,320)(313,319)(314,318)(315,317)(327,330)(328,329)(331,346)(332,350)
(333,349)(334,348)(335,347)(336,341)(337,345)(338,344)(339,343)(340,342)
(352,355)(353,354)(356,371)(357,375)(358,374)(359,373)(360,372)(361,366)
(362,370)(363,369)(364,368)(365,367)(377,380)(378,379)(381,396)(382,400)
(383,399)(384,398)(385,397)(386,391)(387,395)(388,394)(389,393)(390,392);;
s1 := ( 1,207)( 2,206)( 3,210)( 4,209)( 5,208)( 6,202)( 7,201)( 8,205)
( 9,204)( 10,203)( 11,222)( 12,221)( 13,225)( 14,224)( 15,223)( 16,217)
( 17,216)( 18,220)( 19,219)( 20,218)( 21,212)( 22,211)( 23,215)( 24,214)
( 25,213)( 26,232)( 27,231)( 28,235)( 29,234)( 30,233)( 31,227)( 32,226)
( 33,230)( 34,229)( 35,228)( 36,247)( 37,246)( 38,250)( 39,249)( 40,248)
( 41,242)( 42,241)( 43,245)( 44,244)( 45,243)( 46,237)( 47,236)( 48,240)
( 49,239)( 50,238)( 51,257)( 52,256)( 53,260)( 54,259)( 55,258)( 56,252)
( 57,251)( 58,255)( 59,254)( 60,253)( 61,272)( 62,271)( 63,275)( 64,274)
( 65,273)( 66,267)( 67,266)( 68,270)( 69,269)( 70,268)( 71,262)( 72,261)
( 73,265)( 74,264)( 75,263)( 76,282)( 77,281)( 78,285)( 79,284)( 80,283)
( 81,277)( 82,276)( 83,280)( 84,279)( 85,278)( 86,297)( 87,296)( 88,300)
( 89,299)( 90,298)( 91,292)( 92,291)( 93,295)( 94,294)( 95,293)( 96,287)
( 97,286)( 98,290)( 99,289)(100,288)(101,307)(102,306)(103,310)(104,309)
(105,308)(106,302)(107,301)(108,305)(109,304)(110,303)(111,322)(112,321)
(113,325)(114,324)(115,323)(116,317)(117,316)(118,320)(119,319)(120,318)
(121,312)(122,311)(123,315)(124,314)(125,313)(126,332)(127,331)(128,335)
(129,334)(130,333)(131,327)(132,326)(133,330)(134,329)(135,328)(136,347)
(137,346)(138,350)(139,349)(140,348)(141,342)(142,341)(143,345)(144,344)
(145,343)(146,337)(147,336)(148,340)(149,339)(150,338)(151,357)(152,356)
(153,360)(154,359)(155,358)(156,352)(157,351)(158,355)(159,354)(160,353)
(161,372)(162,371)(163,375)(164,374)(165,373)(166,367)(167,366)(168,370)
(169,369)(170,368)(171,362)(172,361)(173,365)(174,364)(175,363)(176,382)
(177,381)(178,385)(179,384)(180,383)(181,377)(182,376)(183,380)(184,379)
(185,378)(186,397)(187,396)(188,400)(189,399)(190,398)(191,392)(192,391)
(193,395)(194,394)(195,393)(196,387)(197,386)(198,390)(199,389)(200,388);;
s2 := ( 6, 21)( 7, 22)( 8, 23)( 9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)
( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)
( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 76)( 52, 77)( 53, 78)( 54, 79)
( 55, 80)( 56, 96)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61, 91)( 62, 92)
( 63, 93)( 64, 94)( 65, 95)( 66, 86)( 67, 87)( 68, 88)( 69, 89)( 70, 90)
( 71, 81)( 72, 82)( 73, 83)( 74, 84)( 75, 85)(101,151)(102,152)(103,153)
(104,154)(105,155)(106,171)(107,172)(108,173)(109,174)(110,175)(111,166)
(112,167)(113,168)(114,169)(115,170)(116,161)(117,162)(118,163)(119,164)
(120,165)(121,156)(122,157)(123,158)(124,159)(125,160)(126,176)(127,177)
(128,178)(129,179)(130,180)(131,196)(132,197)(133,198)(134,199)(135,200)
(136,191)(137,192)(138,193)(139,194)(140,195)(141,186)(142,187)(143,188)
(144,189)(145,190)(146,181)(147,182)(148,183)(149,184)(150,185)(206,221)
(207,222)(208,223)(209,224)(210,225)(211,216)(212,217)(213,218)(214,219)
(215,220)(231,246)(232,247)(233,248)(234,249)(235,250)(236,241)(237,242)
(238,243)(239,244)(240,245)(251,276)(252,277)(253,278)(254,279)(255,280)
(256,296)(257,297)(258,298)(259,299)(260,300)(261,291)(262,292)(263,293)
(264,294)(265,295)(266,286)(267,287)(268,288)(269,289)(270,290)(271,281)
(272,282)(273,283)(274,284)(275,285)(301,351)(302,352)(303,353)(304,354)
(305,355)(306,371)(307,372)(308,373)(309,374)(310,375)(311,366)(312,367)
(313,368)(314,369)(315,370)(316,361)(317,362)(318,363)(319,364)(320,365)
(321,356)(322,357)(323,358)(324,359)(325,360)(326,376)(327,377)(328,378)
(329,379)(330,380)(331,396)(332,397)(333,398)(334,399)(335,400)(336,391)
(337,392)(338,393)(339,394)(340,395)(341,386)(342,387)(343,388)(344,389)
(345,390)(346,381)(347,382)(348,383)(349,384)(350,385);;
s3 := ( 1,101)( 2,102)( 3,103)( 4,104)( 5,105)( 6,106)( 7,107)( 8,108)
( 9,109)( 10,110)( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)( 16,116)
( 17,117)( 18,118)( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)( 24,124)
( 25,125)( 26,126)( 27,127)( 28,128)( 29,129)( 30,130)( 31,131)( 32,132)
( 33,133)( 34,134)( 35,135)( 36,136)( 37,137)( 38,138)( 39,139)( 40,140)
( 41,141)( 42,142)( 43,143)( 44,144)( 45,145)( 46,146)( 47,147)( 48,148)
( 49,149)( 50,150)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)( 56,181)
( 57,182)( 58,183)( 59,184)( 60,185)( 61,186)( 62,187)( 63,188)( 64,189)
( 65,190)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,196)( 72,197)
( 73,198)( 74,199)( 75,200)( 76,151)( 77,152)( 78,153)( 79,154)( 80,155)
( 81,156)( 82,157)( 83,158)( 84,159)( 85,160)( 86,161)( 87,162)( 88,163)
( 89,164)( 90,165)( 91,166)( 92,167)( 93,168)( 94,169)( 95,170)( 96,171)
( 97,172)( 98,173)( 99,174)(100,175)(201,301)(202,302)(203,303)(204,304)
(205,305)(206,306)(207,307)(208,308)(209,309)(210,310)(211,311)(212,312)
(213,313)(214,314)(215,315)(216,316)(217,317)(218,318)(219,319)(220,320)
(221,321)(222,322)(223,323)(224,324)(225,325)(226,326)(227,327)(228,328)
(229,329)(230,330)(231,331)(232,332)(233,333)(234,334)(235,335)(236,336)
(237,337)(238,338)(239,339)(240,340)(241,341)(242,342)(243,343)(244,344)
(245,345)(246,346)(247,347)(248,348)(249,349)(250,350)(251,376)(252,377)
(253,378)(254,379)(255,380)(256,381)(257,382)(258,383)(259,384)(260,385)
(261,386)(262,387)(263,388)(264,389)(265,390)(266,391)(267,392)(268,393)
(269,394)(270,395)(271,396)(272,397)(273,398)(274,399)(275,400)(276,351)
(277,352)(278,353)(279,354)(280,355)(281,356)(282,357)(283,358)(284,359)
(285,360)(286,361)(287,362)(288,363)(289,364)(290,365)(291,366)(292,367)
(293,368)(294,369)(295,370)(296,371)(297,372)(298,373)(299,374)(300,375);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(400)!( 2, 5)( 3, 4)( 6, 21)( 7, 25)( 8, 24)( 9, 23)( 10, 22)
( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)
( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)
( 40, 42)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)
( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)
( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)
( 90, 92)(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)
(111,116)(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)
(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)
(140,142)(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)(160,172)
(161,166)(162,170)(163,169)(164,168)(165,167)(177,180)(178,179)(181,196)
(182,200)(183,199)(184,198)(185,197)(186,191)(187,195)(188,194)(189,193)
(190,192)(202,205)(203,204)(206,221)(207,225)(208,224)(209,223)(210,222)
(211,216)(212,220)(213,219)(214,218)(215,217)(227,230)(228,229)(231,246)
(232,250)(233,249)(234,248)(235,247)(236,241)(237,245)(238,244)(239,243)
(240,242)(252,255)(253,254)(256,271)(257,275)(258,274)(259,273)(260,272)
(261,266)(262,270)(263,269)(264,268)(265,267)(277,280)(278,279)(281,296)
(282,300)(283,299)(284,298)(285,297)(286,291)(287,295)(288,294)(289,293)
(290,292)(302,305)(303,304)(306,321)(307,325)(308,324)(309,323)(310,322)
(311,316)(312,320)(313,319)(314,318)(315,317)(327,330)(328,329)(331,346)
(332,350)(333,349)(334,348)(335,347)(336,341)(337,345)(338,344)(339,343)
(340,342)(352,355)(353,354)(356,371)(357,375)(358,374)(359,373)(360,372)
(361,366)(362,370)(363,369)(364,368)(365,367)(377,380)(378,379)(381,396)
(382,400)(383,399)(384,398)(385,397)(386,391)(387,395)(388,394)(389,393)
(390,392);
s1 := Sym(400)!( 1,207)( 2,206)( 3,210)( 4,209)( 5,208)( 6,202)( 7,201)
( 8,205)( 9,204)( 10,203)( 11,222)( 12,221)( 13,225)( 14,224)( 15,223)
( 16,217)( 17,216)( 18,220)( 19,219)( 20,218)( 21,212)( 22,211)( 23,215)
( 24,214)( 25,213)( 26,232)( 27,231)( 28,235)( 29,234)( 30,233)( 31,227)
( 32,226)( 33,230)( 34,229)( 35,228)( 36,247)( 37,246)( 38,250)( 39,249)
( 40,248)( 41,242)( 42,241)( 43,245)( 44,244)( 45,243)( 46,237)( 47,236)
( 48,240)( 49,239)( 50,238)( 51,257)( 52,256)( 53,260)( 54,259)( 55,258)
( 56,252)( 57,251)( 58,255)( 59,254)( 60,253)( 61,272)( 62,271)( 63,275)
( 64,274)( 65,273)( 66,267)( 67,266)( 68,270)( 69,269)( 70,268)( 71,262)
( 72,261)( 73,265)( 74,264)( 75,263)( 76,282)( 77,281)( 78,285)( 79,284)
( 80,283)( 81,277)( 82,276)( 83,280)( 84,279)( 85,278)( 86,297)( 87,296)
( 88,300)( 89,299)( 90,298)( 91,292)( 92,291)( 93,295)( 94,294)( 95,293)
( 96,287)( 97,286)( 98,290)( 99,289)(100,288)(101,307)(102,306)(103,310)
(104,309)(105,308)(106,302)(107,301)(108,305)(109,304)(110,303)(111,322)
(112,321)(113,325)(114,324)(115,323)(116,317)(117,316)(118,320)(119,319)
(120,318)(121,312)(122,311)(123,315)(124,314)(125,313)(126,332)(127,331)
(128,335)(129,334)(130,333)(131,327)(132,326)(133,330)(134,329)(135,328)
(136,347)(137,346)(138,350)(139,349)(140,348)(141,342)(142,341)(143,345)
(144,344)(145,343)(146,337)(147,336)(148,340)(149,339)(150,338)(151,357)
(152,356)(153,360)(154,359)(155,358)(156,352)(157,351)(158,355)(159,354)
(160,353)(161,372)(162,371)(163,375)(164,374)(165,373)(166,367)(167,366)
(168,370)(169,369)(170,368)(171,362)(172,361)(173,365)(174,364)(175,363)
(176,382)(177,381)(178,385)(179,384)(180,383)(181,377)(182,376)(183,380)
(184,379)(185,378)(186,397)(187,396)(188,400)(189,399)(190,398)(191,392)
(192,391)(193,395)(194,394)(195,393)(196,387)(197,386)(198,390)(199,389)
(200,388);
s2 := Sym(400)!( 6, 21)( 7, 22)( 8, 23)( 9, 24)( 10, 25)( 11, 16)( 12, 17)
( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)
( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 76)( 52, 77)( 53, 78)
( 54, 79)( 55, 80)( 56, 96)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61, 91)
( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66, 86)( 67, 87)( 68, 88)( 69, 89)
( 70, 90)( 71, 81)( 72, 82)( 73, 83)( 74, 84)( 75, 85)(101,151)(102,152)
(103,153)(104,154)(105,155)(106,171)(107,172)(108,173)(109,174)(110,175)
(111,166)(112,167)(113,168)(114,169)(115,170)(116,161)(117,162)(118,163)
(119,164)(120,165)(121,156)(122,157)(123,158)(124,159)(125,160)(126,176)
(127,177)(128,178)(129,179)(130,180)(131,196)(132,197)(133,198)(134,199)
(135,200)(136,191)(137,192)(138,193)(139,194)(140,195)(141,186)(142,187)
(143,188)(144,189)(145,190)(146,181)(147,182)(148,183)(149,184)(150,185)
(206,221)(207,222)(208,223)(209,224)(210,225)(211,216)(212,217)(213,218)
(214,219)(215,220)(231,246)(232,247)(233,248)(234,249)(235,250)(236,241)
(237,242)(238,243)(239,244)(240,245)(251,276)(252,277)(253,278)(254,279)
(255,280)(256,296)(257,297)(258,298)(259,299)(260,300)(261,291)(262,292)
(263,293)(264,294)(265,295)(266,286)(267,287)(268,288)(269,289)(270,290)
(271,281)(272,282)(273,283)(274,284)(275,285)(301,351)(302,352)(303,353)
(304,354)(305,355)(306,371)(307,372)(308,373)(309,374)(310,375)(311,366)
(312,367)(313,368)(314,369)(315,370)(316,361)(317,362)(318,363)(319,364)
(320,365)(321,356)(322,357)(323,358)(324,359)(325,360)(326,376)(327,377)
(328,378)(329,379)(330,380)(331,396)(332,397)(333,398)(334,399)(335,400)
(336,391)(337,392)(338,393)(339,394)(340,395)(341,386)(342,387)(343,388)
(344,389)(345,390)(346,381)(347,382)(348,383)(349,384)(350,385);
s3 := Sym(400)!( 1,101)( 2,102)( 3,103)( 4,104)( 5,105)( 6,106)( 7,107)
( 8,108)( 9,109)( 10,110)( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)
( 16,116)( 17,117)( 18,118)( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)
( 24,124)( 25,125)( 26,126)( 27,127)( 28,128)( 29,129)( 30,130)( 31,131)
( 32,132)( 33,133)( 34,134)( 35,135)( 36,136)( 37,137)( 38,138)( 39,139)
( 40,140)( 41,141)( 42,142)( 43,143)( 44,144)( 45,145)( 46,146)( 47,147)
( 48,148)( 49,149)( 50,150)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)
( 56,181)( 57,182)( 58,183)( 59,184)( 60,185)( 61,186)( 62,187)( 63,188)
( 64,189)( 65,190)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,196)
( 72,197)( 73,198)( 74,199)( 75,200)( 76,151)( 77,152)( 78,153)( 79,154)
( 80,155)( 81,156)( 82,157)( 83,158)( 84,159)( 85,160)( 86,161)( 87,162)
( 88,163)( 89,164)( 90,165)( 91,166)( 92,167)( 93,168)( 94,169)( 95,170)
( 96,171)( 97,172)( 98,173)( 99,174)(100,175)(201,301)(202,302)(203,303)
(204,304)(205,305)(206,306)(207,307)(208,308)(209,309)(210,310)(211,311)
(212,312)(213,313)(214,314)(215,315)(216,316)(217,317)(218,318)(219,319)
(220,320)(221,321)(222,322)(223,323)(224,324)(225,325)(226,326)(227,327)
(228,328)(229,329)(230,330)(231,331)(232,332)(233,333)(234,334)(235,335)
(236,336)(237,337)(238,338)(239,339)(240,340)(241,341)(242,342)(243,343)
(244,344)(245,345)(246,346)(247,347)(248,348)(249,349)(250,350)(251,376)
(252,377)(253,378)(254,379)(255,380)(256,381)(257,382)(258,383)(259,384)
(260,385)(261,386)(262,387)(263,388)(264,389)(265,390)(266,391)(267,392)
(268,393)(269,394)(270,395)(271,396)(272,397)(273,398)(274,399)(275,400)
(276,351)(277,352)(278,353)(279,354)(280,355)(281,356)(282,357)(283,358)
(284,359)(285,360)(286,361)(287,362)(288,363)(289,364)(290,365)(291,366)
(292,367)(293,368)(294,369)(295,370)(296,371)(297,372)(298,373)(299,374)
(300,375);
poly := sub<Sym(400)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope